The business secretary, Vince Cable, says the government’s cap on immigration has been 'very damaging' to British industry. Photograph: Anna Gowthorpe/PA

The government's cap on immigration has been "very damaging" to British industry by stopping companies hiring key staff, the business secretary, Vince Cable, said today.

The Department for Business had examples of companies which had reduced investment or relocated operations overseas because the cap prevented them accessing key staff, said Cable, who called for more flexibility on allowing skilled workers into the UK.

The business secretary has made little secret of his opposition to the cap, which was a key plank of the Conservative manifesto and accepted grudgingly by the Liberal Democrats when they went into coalition in May.

Cable was speaking ahead of next week's Lib Dem conference in Liverpool, at which tensions between the party's activists and its leadership are expected to surface over issues such as immigration and spending cuts.

In a video interview with the Financial Times, Cable acknowledged that there were anxieties in the party which would be aired at conference.

He voiced his own concerns about a cap on visas for workers from outside the EU, launched in interim form in July ahead of the introduction of a permanent limit next April.

"Of course I'm part of the government and we have a policy that we all subscribe to, which is that there has to be an overall cap on migration from outside the European Union," Cable said.

"Nonetheless, I am the business secretary and I have to represent business and the contribution that business makes to the British economy.

"The brutal fact is that the way the system is currently being applied is very damaging.

"We have now lots of case studies of companies which are either not investing or relocating or in many cases just not able to function effectively because they cannot get key staff – management, specialist engineers and so on – from outside the European Union.

"There's no point concealing the fact that this is actually damaging to the UK economy. It affects universities and other institutions which need access to the best people in the world.

"If we are going to be an open economy, thinking globally and acting globally, we have to be flexible in the way that we treat people of this kind."

Cable declined to name companies that have complained, but said they included the investment banking, engineering and pharmaceuticals sectors.

In one case, a UK company needed 500 specialist engineers but was given a quota of four. Cable said he had spoken to an entrepreneur who scrapped plans to open a factory and create 400 jobs in northern England after failing to secure visas for key staff.

The shadow business secretary, Pat McFadden, said Cable was right to say that the government's proposed immigration cap was damaging British industry.

"The idea that a global trading nation like ours should stop talent from overseas coming to work or study here is good neither for our economy nor for our world-leading position in education and research," he said. "The government is hopelessly at sea on this.

"They have said they want to promote trade, then sent out a signal that talent from overseas is not welcome in the UK.

"Of course there should be proper controls on immigration but an arbitrary cap on net numbers is not the way to do it."

Cable voiced his concerns about the immigration cap during a trade mission to India with David Cameron in July.

Cameron then played down suggestions of a split within the Cabinet, saying: "It is perfectly legitimate for the business secretary to argue for the advantages of free and open markets and that is what Vince does. But we decide these things in the cabinet in a reasonable and sensible way."

The PM's official spokesman told reporters this morning that this remained Cameron's view.

The spokesman said the government was aware of business concerns and would take them into account when setting the level of the permanent cap next year.

But he added: "I don't think that there is evidence that it is doing huge damage to the UK economy."

Asked whether Cable would be given a dressing down for his comments, the spokesman told reporters: "He is raising the concerns of business and we are aware of those concerns and we are keen to implement this policy in a way that allows the brightest and best to come and work in the UK …

"There is a clear coalition policy on this and that was established pretty much on day one.

"The government believes that Britain can benefit from migration but not uncontrolled migration. It is committed to dealing with that issue, but it will look at how this policy and this cap is implemented and endeavour to ensure that the best people are able to come and work in the UK."